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"Accessible to a broad base of readers, Self-Similarity and Beyond illuminates a variety of productive methods for meeting the challenges of nonlinearity. Researchers and graduate students in nonlinearity, partial differential equations, and fluid mechanics, along with mathematical physicists and numerical analysts will rediscover the importance of exact solutions and find valuable additions to their mathematical toolkits."--Jacket.Read more...

Abstract:

Nonlinearity plays a major role in the understanding of most physical, chemical, biological, and engineering sciences. This volume presents a myriad of approaches to finding exact solutions of a variety of nonlinear problems. The presentation includes numerical solutions that motivate or confirm the methods developed.Read more...

Reviews

Editorial reviews

Publisher Synopsis

"The main theme of this book is exact solutions to nonlinear partial differential equations and systematic methods for finding them. All techniques are demonstrated with plenty of worked-out examples, which are predominantly drawn from fluid mechanics, reaction-diffusion systems, and nonlinear diffusionThroughout the book, notation is kept elementary, and the sections are largely independent of each other. This work will serve as a valuable reference for anybody working in applied mathematics and respective areas of application, as well as a source of nontrivial, yet elementary, examples of solutions to nonlinear partial differential equations for teaching purposes." - Mathematical Reviews, Issue 2002 "The methods and their limitations are clearly explained, and are complemented by a number of solved examples focusing on equations in fluid mechanics and nonlinear diffusion." -European Mathematical Society Newsletter, No. 42, December 2001Read more...